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Simulating the M/M/1 Queue

​
initial number of customers
0
mean time between arrivals
3
mean service time
2
seed for random numbers
1
steady-state mean numbers
L
=
2.000
(mean number of customers)
L
q
=
1.333
(mean length of the queue)
W
=
6.000
(mean time in the system)
W
q
=
4.000
(mean time of queueing)
ρ
=
0.667
(server utilization)
This Demonstration shows simulated paths of the M/M/1 queue. Thus, you can see how the number of customers changes with time. You can adjust the initial number of customers, the mean time between arrivals, and the mean service time. The M/M/1 queue is an example of a continuous-time Markov chain.
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